You are given an integer n and a threshold integer k. Your task is to form the smallest number possible from the digits of n by deleting some digits, while maintaining the original order of the digits. The formed number must be greater than k.

Details:

You must preserve the order of the digits from n.

If the smallest number you can form is less than or equal to k, try to include additional digits from n to ensure the result is greater than k.

Function Signature:

string smallestNumberGreaterThanK(string numStr, int k);